Median Absolute Deviation Calculator
The most robust spread measure there is — the median of the distances from the median, which half your data can be corrupted before it moves.
Take the median, find each value's absolute distance from it, then take the median of those distances.
How the median absolute deviation calculator works
Take the median, find each value's absolute distance from it, then take the median of those distances. Because both steps are medians, the result has a breakdown point of 50%: it takes more than half the data being wrong to break it.
Multiplying by 1.4826 scales it to estimate σ for normal data, which is how it is used as a drop-in robust replacement for the standard deviation.
Formula: MAD = median(|xᵢ − median(x)|); σ̂ = 1.4826 × MAD
Worked examples
| Inputs | Median absolute deviation | Note |
|---|---|---|
| Seven ordinary values and one of 1000 | 2 | MAD = 2, SD = 352 — the outlier is caught |
| Clean data | 2 | MAD = 2, robust σ ≈ 2.97 |
| Identical values | 0 | MAD = 0 |
FAQFrequently asked questions
What is the median absolute deviation?
The median of the absolute distances from the median — a spread measure that ignores extremes completely.
Why 1.4826?
It is 1 ÷ Φ⁻¹(0.75), the factor that makes the MAD estimate σ for normally distributed data.
What is a breakdown point?
The fraction of the data that can be arbitrarily corrupted before the statistic becomes meaningless. The mean's is 0%; the MAD's is 50% — the highest possible.
When should I use it?
Any time outliers are plausible and you cannot inspect every point — sensor data, log timings, scraped measurements.
Is it the same as mean absolute deviation?
No, and the shared acronym causes real confusion. That one averages distances from the mean; this one takes the median of distances from the median.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.